Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def search(n, arr):
    start, end = 0, l-1
    while start <= end:
        mid = (start + end) // 2
        if arr[mid] == n:
            return True
        elif n <= arr[mid]:
            end = mid-1
        else:
            start = mid+1
    return False

n = int(input())
funky = []
i = 1
while True:
    num = i*(i+1) // 2
    if num <= n:
        funky.append(num)
    else:
        break
    i += 1
l = len(funky)

i, flag = 1, False
while i*i <= n:
    complement = n - (i*(i+1)) // 2
    if search(complement, funky):
        flag = True
        break
    i += 1
print("YES" if flag else "NO")